Mercurial > octave-nkf
annotate doc/interpreter/numbers.txi @ 19627:446c46af4b42 stable
strip trailing whitespace from most source files
* Makefile.am, NEWS, build-aux/common.mk, configure.ac,
doc/Makefile.am, doc/doxyhtml/Makefile.am,
doc/interpreter/Makefile.am, doc/interpreter/arith.txi,
doc/interpreter/audio.txi, doc/interpreter/basics.txi,
doc/interpreter/bugs.txi, doc/interpreter/container.txi,
doc/interpreter/cp-idx.txi, doc/interpreter/data.txi,
doc/interpreter/debug.txi, doc/interpreter/diagperm.txi,
doc/interpreter/diffeq.txi, doc/interpreter/doccheck/README,
doc/interpreter/doccheck/spellcheck, doc/interpreter/emacs.txi,
doc/interpreter/errors.txi, doc/interpreter/eval.txi,
doc/interpreter/expr.txi, doc/interpreter/external.txi,
doc/interpreter/fn-idx.txi, doc/interpreter/func.txi,
doc/interpreter/geometry.txi, doc/interpreter/geometryimages.m,
doc/interpreter/gpl.txi, doc/interpreter/grammar.txi,
doc/interpreter/gui.txi, doc/interpreter/image.txi,
doc/interpreter/install.txi, doc/interpreter/interp.txi,
doc/interpreter/interpimages.m, doc/interpreter/intro.txi,
doc/interpreter/io.txi, doc/interpreter/java.txi,
doc/interpreter/linalg.txi, doc/interpreter/macros.texi,
doc/interpreter/matrix.txi, doc/interpreter/munge-texi.pl,
doc/interpreter/nonlin.txi, doc/interpreter/numbers.txi,
doc/interpreter/obsolete.txi, doc/interpreter/octave-config.1,
doc/interpreter/octave.texi, doc/interpreter/oop.txi,
doc/interpreter/op-idx.txi, doc/interpreter/optim.txi,
doc/interpreter/package.txi, doc/interpreter/plot.txi,
doc/interpreter/poly.txi, doc/interpreter/preface.txi,
doc/interpreter/quad.txi, doc/interpreter/set.txi,
doc/interpreter/signal.txi, doc/interpreter/sparse.txi,
doc/interpreter/sparseimages.m, doc/interpreter/splineimages.m,
doc/interpreter/stats.txi, doc/interpreter/stmt.txi,
doc/interpreter/strings.txi, doc/interpreter/system.txi,
doc/interpreter/testfun.txi, doc/interpreter/tips.txi,
doc/interpreter/var.txi, doc/interpreter/vectorize.txi,
doc/liboctave/Makefile.am, doc/liboctave/array.texi,
doc/liboctave/bugs.texi, doc/liboctave/cp-idx.texi,
doc/liboctave/dae.texi, doc/liboctave/diffeq.texi,
doc/liboctave/error.texi, doc/liboctave/factor.texi,
doc/liboctave/fn-idx.texi, doc/liboctave/gpl.texi,
doc/liboctave/install.texi, doc/liboctave/intro.texi,
doc/liboctave/liboctave.texi, doc/liboctave/matvec.texi,
doc/liboctave/nleqn.texi, doc/liboctave/nlfunc.texi,
doc/liboctave/ode.texi, doc/liboctave/optim.texi,
doc/liboctave/preface.texi, doc/liboctave/quad.texi,
doc/liboctave/range.texi, doc/refcard/Makefile.am,
doc/refcard/refcard.tex, etc/HACKING, etc/NEWS.1, etc/NEWS.2,
etc/NEWS.3, etc/OLD-ChangeLogs/ChangeLog,
etc/OLD-ChangeLogs/doc-ChangeLog,
etc/OLD-ChangeLogs/scripts-ChangeLog,
etc/OLD-ChangeLogs/src-ChangeLog, etc/OLD-ChangeLogs/test-ChangeLog,
etc/PROJECTS, etc/README.Cygwin, etc/README.MacOS, etc/README.MinGW,
etc/README.gnuplot, etc/gdbinit, etc/icons/Makefile.am,
examples/@polynomial/end.m, examples/@polynomial/subsasgn.m,
examples/Makefile.am, examples/standalonebuiltin.cc,
libgui/Makefile.am, libgui/qterminal/libqterminal/README,
libgui/qterminal/libqterminal/unix/BlockArray.cpp,
libgui/qterminal/libqterminal/unix/BlockArray.h,
libgui/qterminal/libqterminal/unix/Character.h,
libgui/qterminal/libqterminal/unix/CharacterColor.h,
libgui/qterminal/libqterminal/unix/Emulation.cpp,
libgui/qterminal/libqterminal/unix/Emulation.h,
libgui/qterminal/libqterminal/unix/Filter.cpp,
libgui/qterminal/libqterminal/unix/Filter.h,
libgui/qterminal/libqterminal/unix/History.cpp,
libgui/qterminal/libqterminal/unix/History.h,
libgui/qterminal/libqterminal/unix/KeyboardTranslator.cpp,
libgui/qterminal/libqterminal/unix/KeyboardTranslator.h,
libgui/qterminal/libqterminal/unix/LineFont.h,
libgui/qterminal/libqterminal/unix/QUnixTerminalImpl.cpp,
libgui/qterminal/libqterminal/unix/QUnixTerminalImpl.h,
libgui/qterminal/libqterminal/unix/Screen.cpp,
libgui/qterminal/libqterminal/unix/Screen.h,
libgui/qterminal/libqterminal/unix/ScreenWindow.cpp,
libgui/qterminal/libqterminal/unix/ScreenWindow.h,
libgui/qterminal/libqterminal/unix/TerminalCharacterDecoder.cpp,
libgui/qterminal/libqterminal/unix/TerminalCharacterDecoder.h,
libgui/qterminal/libqterminal/unix/Vt102Emulation.h,
libgui/qterminal/libqterminal/win32/QWinTerminalImpl.cpp,
libgui/qterminal/qterminal/main.cpp,
libgui/src/m-editor/file-editor-tab.cc, libgui/src/octave-gui.cc,
libgui/src/octave-qt-link.cc, libinterp/corefcn/data.cc,
libinterp/corefcn/defun-int.h, libinterp/corefcn/det.cc,
libinterp/corefcn/gl2ps-renderer.cc, libinterp/corefcn/graphics.cc,
libinterp/corefcn/graphics.in.h, libinterp/corefcn/ls-mat5.cc,
libinterp/corefcn/lu.cc, libinterp/corefcn/oct-tex-parser.yy,
libinterp/corefcn/oct-tex-symbols.in, libinterp/corefcn/quadcc.cc,
libinterp/corefcn/zfstream.cc, libinterp/dldfcn/__eigs__.cc,
libinterp/dldfcn/__voronoi__.cc, libinterp/gendoc.pl,
libinterp/genprops.awk, libinterp/mk-errno-list, libinterp/mk-pkg-add,
libinterp/mkbuiltins, libinterp/mkdefs, libinterp/mkdocs,
libinterp/mkops, libinterp/octave-value/ov-java.cc,
libinterp/parse-tree/lex.ll, libinterp/parse-tree/oct-parse.in.yy,
libinterp/parse-tree/octave.gperf, liboctave/Makefile.am,
liboctave/array/Array.cc, liboctave/array/module.mk,
liboctave/cruft/daspk/datv.f, liboctave/cruft/daspk/dcnst0.f,
liboctave/cruft/daspk/dcnstr.f, liboctave/cruft/daspk/ddasic.f,
liboctave/cruft/daspk/ddasid.f, liboctave/cruft/daspk/ddasik.f,
liboctave/cruft/daspk/ddaspk.f, liboctave/cruft/daspk/ddstp.f,
liboctave/cruft/daspk/ddwnrm.f, liboctave/cruft/daspk/dfnrmd.f,
liboctave/cruft/daspk/dfnrmk.f, liboctave/cruft/daspk/dhels.f,
liboctave/cruft/daspk/dheqr.f, liboctave/cruft/daspk/dinvwt.f,
liboctave/cruft/daspk/dlinsd.f, liboctave/cruft/daspk/dlinsk.f,
liboctave/cruft/daspk/dmatd.f, liboctave/cruft/daspk/dnedd.f,
liboctave/cruft/daspk/dnedk.f, liboctave/cruft/daspk/dnsd.f,
liboctave/cruft/daspk/dnsid.f, liboctave/cruft/daspk/dnsik.f,
liboctave/cruft/daspk/dnsk.f, liboctave/cruft/daspk/dorth.f,
liboctave/cruft/daspk/dslvd.f, liboctave/cruft/daspk/dslvk.f,
liboctave/cruft/daspk/dspigm.f, liboctave/cruft/daspk/dyypnw.f,
liboctave/cruft/dasrt/ddasrt.f, liboctave/cruft/dasrt/drchek.f,
liboctave/cruft/dassl/ddaslv.f, liboctave/cruft/dassl/ddassl.f,
liboctave/cruft/misc/blaswrap.c, liboctave/cruft/misc/module.mk,
liboctave/cruft/odepack/cfode.f, liboctave/cruft/odepack/dlsode.f,
liboctave/cruft/odepack/ewset.f, liboctave/cruft/odepack/intdy.f,
liboctave/cruft/odepack/prepj.f, liboctave/cruft/odepack/sintdy.f,
liboctave/cruft/odepack/slsode.f, liboctave/cruft/odepack/solsy.f,
liboctave/cruft/odepack/ssolsy.f, liboctave/cruft/odepack/stode.f,
liboctave/cruft/odepack/vnorm.f, liboctave/cruft/ranlib/Basegen.doc,
liboctave/cruft/ranlib/README, liboctave/cruft/ranlib/genbet.f,
liboctave/cruft/ranlib/genexp.f, liboctave/cruft/ranlib/gennch.f,
liboctave/cruft/ranlib/gennf.f, liboctave/cruft/ranlib/gennor.f,
liboctave/cruft/ranlib/getsd.f, liboctave/cruft/ranlib/initgn.f,
liboctave/cruft/ranlib/phrtsd.f, liboctave/cruft/ranlib/randlib.fdoc,
liboctave/cruft/ranlib/setsd.f, liboctave/cruft/ranlib/tstgmn.for,
liboctave/cruft/ranlib/tstmid.for, liboctave/cruft/slatec-fn/atanh.f,
liboctave/cruft/slatec-fn/datanh.f,
liboctave/cruft/slatec-fn/xgmainc.f,
liboctave/cruft/slatec-fn/xsgmainc.f, liboctave/numeric/module.mk,
liboctave/operators/mk-ops.awk, liboctave/operators/mx-ops,
liboctave/operators/sparse-mk-ops.awk,
liboctave/operators/sparse-mx-ops, liboctave/operators/vx-ops,
liboctave/util/module.mk, run-octave.in, scripts/@ftp/ftp.m,
scripts/audio/wavread.m, scripts/deprecated/java_convert_matrix.m,
scripts/deprecated/java_debug.m, scripts/deprecated/java_invoke.m,
scripts/deprecated/java_new.m,
scripts/deprecated/java_unsigned_conversion.m,
scripts/deprecated/javafields.m, scripts/deprecated/javamethods.m,
scripts/deprecated/shell_cmd.m, scripts/general/accumarray.m,
scripts/general/display.m, scripts/general/fieldnames.m,
scripts/general/interp1.m, scripts/general/interp2.m,
scripts/general/interp3.m, scripts/general/isa.m,
scripts/general/methods.m, scripts/general/sortrows.m,
scripts/geometry/convhull.m, scripts/geometry/delaunay.m,
scripts/geometry/delaunay3.m, scripts/geometry/delaunayn.m,
scripts/geometry/griddata.m, scripts/geometry/griddatan.m,
scripts/geometry/voronoi.m, scripts/geometry/voronoin.m,
scripts/gui/guihandles.m, scripts/gui/inputdlg.m,
scripts/gui/listdlg.m, scripts/gui/msgbox.m, scripts/gui/questdlg.m,
scripts/gui/uigetfile.m, scripts/gui/waitbar.m, scripts/gui/warndlg.m,
scripts/help/doc.m, scripts/help/help.m, scripts/help/type.m,
scripts/image/bone.m, scripts/image/cmpermute.m,
scripts/image/cmunique.m, scripts/image/colorcube.m,
scripts/image/colormap.m, scripts/image/contrast.m,
scripts/image/gray2ind.m, scripts/image/image.m,
scripts/image/imshow.m, scripts/image/ind2gray.m, scripts/image/jet.m,
scripts/image/rgb2ntsc.m, scripts/image/spinmap.m,
scripts/io/importdata.m, scripts/io/strread.m, scripts/io/textread.m,
scripts/io/textscan.m, scripts/java/java_get.m,
scripts/java/java_set.m, scripts/java/javaaddpath.m,
scripts/java/javaclasspath.m, scripts/java/javamem.m,
scripts/linear-algebra/linsolve.m, scripts/linear-algebra/qzhess.m,
scripts/miscellaneous/debug.m, scripts/miscellaneous/desktop.m,
scripts/miscellaneous/dir.m, scripts/miscellaneous/dos.m,
scripts/miscellaneous/edit.m, scripts/miscellaneous/fact.m,
scripts/miscellaneous/getappdata.m, scripts/miscellaneous/inputname.m,
scripts/miscellaneous/license.m, scripts/miscellaneous/ls_command.m,
scripts/miscellaneous/run.m, scripts/miscellaneous/setfield.m,
scripts/miscellaneous/unix.m, scripts/miscellaneous/ver.m,
scripts/mk-pkg-add, scripts/mkdoc.pl,
scripts/optimization/fminsearch.m, scripts/optimization/optimset.m,
scripts/optimization/sqp.m, scripts/pkg/pkg.m,
scripts/pkg/private/create_pkgadddel.m,
scripts/pkg/private/fix_depends.m, scripts/pkg/private/install.m,
scripts/plot/appearance/axis.m, scripts/plot/appearance/box.m,
scripts/plot/appearance/clabel.m, scripts/plot/appearance/daspect.m,
scripts/plot/appearance/datetick.m, scripts/plot/appearance/grid.m,
scripts/plot/appearance/legend.m, scripts/plot/appearance/orient.m,
scripts/plot/appearance/shading.m, scripts/plot/appearance/text.m,
scripts/plot/appearance/title.m, scripts/plot/appearance/xlabel.m,
scripts/plot/appearance/ylabel.m, scripts/plot/appearance/zlabel.m,
scripts/plot/draw/area.m, scripts/plot/draw/bar.m,
scripts/plot/draw/barh.m, scripts/plot/draw/colorbar.m,
scripts/plot/draw/contour.m, scripts/plot/draw/contour3.m,
scripts/plot/draw/contourf.m, scripts/plot/draw/ellipsoid.m,
scripts/plot/draw/errorbar.m, scripts/plot/draw/ezcontour.m,
scripts/plot/draw/ezcontourf.m, scripts/plot/draw/ezmesh.m,
scripts/plot/draw/ezpolar.m, scripts/plot/draw/fill.m,
scripts/plot/draw/fplot.m, scripts/plot/draw/hist.m,
scripts/plot/draw/meshc.m, scripts/plot/draw/meshz.m,
scripts/plot/draw/pareto.m, scripts/plot/draw/patch.m,
scripts/plot/draw/peaks.m, scripts/plot/draw/pie.m,
scripts/plot/draw/pie3.m, scripts/plot/draw/plot.m,
scripts/plot/draw/plotyy.m, scripts/plot/draw/private/__bar__.m,
scripts/plot/draw/private/__contour__.m,
scripts/plot/draw/private/__errplot__.m,
scripts/plot/draw/private/__ezplot__.m,
scripts/plot/draw/private/__patch__.m,
scripts/plot/draw/private/__stem__.m, scripts/plot/draw/rectangle.m,
scripts/plot/draw/ribbon.m, scripts/plot/draw/rose.m,
scripts/plot/draw/scatter.m, scripts/plot/draw/scatter3.m,
scripts/plot/draw/semilogx.m, scripts/plot/draw/shrinkfaces.m,
scripts/plot/draw/sombrero.m, scripts/plot/draw/sphere.m,
scripts/plot/draw/stairs.m, scripts/plot/draw/stem.m,
scripts/plot/draw/stemleaf.m, scripts/plot/draw/surf.m,
scripts/plot/draw/surface.m, scripts/plot/draw/surfc.m,
scripts/plot/draw/surfl.m, scripts/plot/draw/surfnorm.m,
scripts/plot/draw/tetramesh.m, scripts/plot/draw/trimesh.m,
scripts/plot/draw/triplot.m, scripts/plot/draw/trisurf.m,
scripts/plot/util/__gnuplot_drawnow__.m,
scripts/plot/util/__plt_get_axis_arg__.m, scripts/plot/util/axes.m,
scripts/plot/util/clf.m, scripts/plot/util/copyobj.m,
scripts/plot/util/figure.m, scripts/plot/util/gcbo.m,
scripts/plot/util/graphics_toolkit.m, scripts/plot/util/hggroup.m,
scripts/plot/util/meshgrid.m, scripts/plot/util/newplot.m,
scripts/plot/util/print.m,
scripts/plot/util/private/__add_default_menu__.m,
scripts/plot/util/private/__fltk_print__.m,
scripts/plot/util/private/__gnuplot_print__.m,
scripts/plot/util/private/__print_parse_opts__.m,
scripts/plot/util/refreshdata.m, scripts/plot/util/subplot.m,
scripts/polynomial/conv.m, scripts/polynomial/poly.m,
scripts/polynomial/polyeig.m, scripts/polynomial/polyfit.m,
scripts/polynomial/polyval.m,
scripts/polynomial/private/__splinefit__.m,
scripts/polynomial/spline.m, scripts/prefs/prefdir.m,
scripts/prefs/preferences.m, scripts/prefs/private/prefsfile.m,
scripts/prefs/rmpref.m, scripts/signal/freqz.m,
scripts/signal/module.mk, scripts/sparse/eigs.m, scripts/sparse/pcg.m,
scripts/sparse/private/__sprand_impl__.m, scripts/sparse/sprand.m,
scripts/sparse/sprandn.m, scripts/sparse/spy.m, scripts/sparse/svds.m,
scripts/specfun/expint.m, scripts/specfun/factor.m,
scripts/special-matrix/gallery.m, scripts/special-matrix/hankel.m,
scripts/special-matrix/toeplitz.m, scripts/startup/inputrc,
scripts/statistics/base/kurtosis.m, scripts/statistics/base/moment.m,
scripts/statistics/base/qqplot.m, scripts/statistics/base/var.m,
scripts/statistics/distributions/betarnd.m,
scripts/statistics/distributions/binoinv.m,
scripts/statistics/distributions/binopdf.m,
scripts/statistics/distributions/binornd.m,
scripts/statistics/distributions/cauchy_rnd.m,
scripts/statistics/distributions/chi2rnd.m,
scripts/statistics/distributions/discrete_pdf.m,
scripts/statistics/distributions/discrete_rnd.m,
scripts/statistics/distributions/empirical_rnd.m,
scripts/statistics/distributions/exprnd.m,
scripts/statistics/distributions/frnd.m,
scripts/statistics/distributions/gamrnd.m,
scripts/statistics/distributions/geornd.m,
scripts/statistics/distributions/hygernd.m,
scripts/statistics/distributions/kolmogorov_smirnov_cdf.m,
scripts/statistics/distributions/laplace_cdf.m,
scripts/statistics/distributions/laplace_pdf.m,
scripts/statistics/distributions/logistic_cdf.m,
scripts/statistics/distributions/logistic_pdf.m,
scripts/statistics/distributions/lognrnd.m,
scripts/statistics/distributions/nbincdf.m,
scripts/statistics/distributions/nbininv.m,
scripts/statistics/distributions/nbinpdf.m,
scripts/statistics/distributions/nbinrnd.m,
scripts/statistics/distributions/normrnd.m,
scripts/statistics/distributions/poissinv.m,
scripts/statistics/distributions/poissrnd.m,
scripts/statistics/distributions/tinv.m,
scripts/statistics/distributions/trnd.m,
scripts/statistics/distributions/unidcdf.m,
scripts/statistics/distributions/unidpdf.m,
scripts/statistics/distributions/unidrnd.m,
scripts/statistics/distributions/unifrnd.m,
scripts/statistics/distributions/wblrnd.m,
scripts/statistics/models/module.mk,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/strings/base2dec.m, scripts/strings/deblank.m,
scripts/strings/dec2base.m, scripts/strings/dec2bin.m,
scripts/strings/dec2hex.m, scripts/strings/mat2str.m,
scripts/strings/ostrsplit.m, scripts/strings/regexptranslate.m,
scripts/strings/str2num.m, scripts/strings/strcat.m,
scripts/strings/strjoin.m, scripts/strings/strsplit.m,
scripts/strings/strtok.m, scripts/strings/strtrim.m,
scripts/strings/strtrunc.m, scripts/strings/substr.m,
scripts/testfun/__run_test_suite__.m, scripts/testfun/speed.m,
scripts/testfun/test.m, scripts/time/asctime.m,
scripts/time/datenum.m, scripts/time/datevec.m,
scripts/time/weekday.m, src/Makefile.am, test/Makefile.am,
test/build-bc-overload-tests.sh, test/build-sparse-tests.sh,
test/jit.tst, test/line-continue.tst: Strip trailing whitespace.
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Tue, 20 Jan 2015 08:26:57 -0500 |
| parents | d63878346099 |
| children | 0e1f5a750d00 |
| rev | line source |
|---|---|
|
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1 @c Copyright (C) 1996-2013 John W. Eaton |
| 7018 | 2 @c |
| 3 @c This file is part of Octave. | |
| 4 @c | |
| 5 @c Octave is free software; you can redistribute it and/or modify it | |
| 6 @c under the terms of the GNU General Public License as published by the | |
| 7 @c Free Software Foundation; either version 3 of the License, or (at | |
| 8 @c your option) any later version. | |
|
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9 @c |
| 7018 | 10 @c Octave is distributed in the hope that it will be useful, but WITHOUT |
| 11 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 12 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 13 @c for more details. | |
|
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14 @c |
| 7018 | 15 @c You should have received a copy of the GNU General Public License |
| 16 @c along with Octave; see the file COPYING. If not, see | |
| 17 @c <http://www.gnu.org/licenses/>. | |
| 3294 | 18 |
| 4167 | 19 @node Numeric Data Types |
| 3294 | 20 @chapter Numeric Data Types |
| 21 @cindex numeric constant | |
| 22 @cindex numeric value | |
| 23 | |
| 24 A @dfn{numeric constant} may be a scalar, a vector, or a matrix, and it | |
| 25 may contain complex values. | |
| 26 | |
| 27 The simplest form of a numeric constant, a scalar, is a single number | |
| 28 that can be an integer, a decimal fraction, a number in scientific | |
| 6620 | 29 (exponential) notation, or a complex number. Note that by default numeric |
| 3294 | 30 constants are represented within Octave in double-precision floating |
| 31 point format (complex constants are stored as pairs of double-precision | |
|
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32 floating point values). It is, however, possible to represent real |
|
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33 integers as described in @ref{Integer Data Types}. Here are some |
|
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34 examples of real-valued numeric constants, which all have the same |
|
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35 value: |
| 3294 | 36 |
| 37 @example | |
| 38 @group | |
| 39 105 | |
| 40 1.05e+2 | |
| 41 1050e-1 | |
| 42 @end group | |
| 43 @end example | |
| 44 | |
| 45 To specify complex constants, you can write an expression of the form | |
| 46 | |
| 47 @example | |
| 48 @group | |
| 49 3 + 4i | |
| 50 3.0 + 4.0i | |
| 51 0.3e1 + 40e-1i | |
| 52 @end group | |
| 53 @end example | |
| 54 | |
| 6620 | 55 @noindent |
| 3294 | 56 all of which are equivalent. The letter @samp{i} in the previous example |
| 57 stands for the pure imaginary constant, defined as | |
| 58 @tex | |
| 59 $\sqrt{-1}$. | |
| 60 @end tex | |
| 6620 | 61 @ifnottex |
| 3294 | 62 @code{sqrt (-1)}. |
| 6620 | 63 @end ifnottex |
| 3294 | 64 |
| 65 For Octave to recognize a value as the imaginary part of a complex | |
| 66 constant, a space must not appear between the number and the @samp{i}. | |
| 67 If it does, Octave will print an error message, like this: | |
| 68 | |
| 69 @example | |
| 70 @group | |
| 71 octave:13> 3 + 4 i | |
| 72 | |
| 73 parse error: | |
| 74 | |
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75 syntax error |
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76 |
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77 >>> 3 + 4 i |
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78 ^ |
| 3294 | 79 @end group |
| 80 @end example | |
| 81 | |
| 6620 | 82 @noindent |
| 3294 | 83 You may also use @samp{j}, @samp{I}, or @samp{J} in place of the |
| 84 @samp{i} above. All four forms are equivalent. | |
| 85 | |
| 6549 | 86 @DOCSTRING(double) |
| 87 | |
| 88 @DOCSTRING(complex) | |
| 89 | |
| 3294 | 90 @menu |
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91 * Matrices:: |
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92 * Ranges:: |
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93 * Single Precision Data Types:: |
| 6549 | 94 * Integer Data Types:: |
| 6781 | 95 * Bit Manipulations:: |
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96 * Logical Values:: |
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97 * Promotion and Demotion of Data Types:: |
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98 * Predicates for Numeric Objects:: |
| 3294 | 99 @end menu |
| 100 | |
| 4167 | 101 @node Matrices |
| 3294 | 102 @section Matrices |
| 103 @cindex matrices | |
| 104 | |
| 105 @opindex [ | |
| 106 @opindex ] | |
| 107 @opindex ; | |
| 108 @opindex , | |
| 109 | |
| 110 It is easy to define a matrix of values in Octave. The size of the | |
| 111 matrix is determined automatically, so it is not necessary to explicitly | |
| 112 state the dimensions. The expression | |
| 113 | |
| 114 @example | |
| 115 a = [1, 2; 3, 4] | |
| 116 @end example | |
| 117 | |
| 118 @noindent | |
| 119 results in the matrix | |
| 120 @tex | |
| 121 $$ a = \left[ \matrix{ 1 & 2 \cr 3 & 4 } \right] $$ | |
| 122 @end tex | |
| 6620 | 123 @ifnottex |
| 3294 | 124 |
| 125 @example | |
| 126 @group | |
| 127 | |
| 128 / \ | |
| 129 | 1 2 | | |
| 130 a = | | | |
| 131 | 3 4 | | |
| 132 \ / | |
| 133 | |
| 134 @end group | |
| 135 @end example | |
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136 |
| 6620 | 137 @end ifnottex |
| 3294 | 138 |
| 139 Elements of a matrix may be arbitrary expressions, provided that the | |
| 140 dimensions all make sense when combining the various pieces. For | |
| 141 example, given the above matrix, the expression | |
| 142 | |
| 143 @example | |
| 144 [ a, a ] | |
| 145 @end example | |
| 146 | |
| 147 @noindent | |
| 148 produces the matrix | |
| 149 | |
| 150 @example | |
| 151 @group | |
| 152 ans = | |
| 153 | |
| 154 1 2 1 2 | |
| 155 3 4 3 4 | |
| 156 @end group | |
| 157 @end example | |
| 158 | |
| 159 @noindent | |
| 160 but the expression | |
| 161 | |
| 162 @example | |
| 163 [ a, 1 ] | |
| 164 @end example | |
| 165 | |
| 166 @noindent | |
| 167 produces the error | |
| 168 | |
| 169 @example | |
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170 error: number of rows must match (1 != 2) near line 13, column 6 |
| 3294 | 171 @end example |
| 172 | |
| 173 @noindent | |
| 174 (assuming that this expression was entered as the first thing on line | |
| 175 13, of course). | |
| 176 | |
| 177 Inside the square brackets that delimit a matrix expression, Octave | |
| 178 looks at the surrounding context to determine whether spaces and newline | |
| 179 characters should be converted into element and row separators, or | |
| 4476 | 180 simply ignored, so an expression like |
| 3294 | 181 |
| 182 @example | |
| 183 @group | |
| 184 a = [ 1 2 | |
| 185 3 4 ] | |
| 186 @end group | |
| 187 @end example | |
| 188 | |
| 189 @noindent | |
| 190 will work. However, some possible sources of confusion remain. For | |
| 191 example, in the expression | |
| 192 | |
| 193 @example | |
| 194 [ 1 - 1 ] | |
| 195 @end example | |
| 196 | |
| 197 @noindent | |
| 198 the @samp{-} is treated as a binary operator and the result is the | |
| 199 scalar 0, but in the expression | |
| 200 | |
| 201 @example | |
| 202 [ 1 -1 ] | |
| 203 @end example | |
| 204 | |
| 205 @noindent | |
| 206 the @samp{-} is treated as a unary operator and the result is the | |
| 4476 | 207 vector @code{[ 1, -1 ]}. Similarly, the expression |
| 208 | |
| 209 @example | |
| 210 [ sin (pi) ] | |
| 211 @end example | |
| 212 | |
| 213 @noindent | |
| 214 will be parsed as | |
| 215 | |
| 216 @example | |
| 217 [ sin, (pi) ] | |
| 218 @end example | |
| 3294 | 219 |
| 4476 | 220 @noindent |
| 221 and will result in an error since the @code{sin} function will be | |
| 222 called with no arguments. To get around this, you must omit the space | |
| 223 between @code{sin} and the opening parenthesis, or enclose the | |
| 224 expression in a set of parentheses: | |
| 225 | |
| 226 @example | |
| 227 [ (sin (pi)) ] | |
| 228 @end example | |
| 229 | |
| 230 Whitespace surrounding the single quote character (@samp{'}, used as a | |
| 231 transpose operator and for delimiting character strings) can also cause | |
| 232 confusion. Given @code{a = 1}, the expression | |
| 3294 | 233 |
| 234 @example | |
| 235 [ 1 a' ] | |
| 236 @end example | |
| 237 | |
| 238 @noindent | |
| 4476 | 239 results in the single quote character being treated as a |
| 3294 | 240 transpose operator and the result is the vector @code{[ 1, 1 ]}, but the |
| 241 expression | |
| 242 | |
| 243 @example | |
| 244 [ 1 a ' ] | |
| 245 @end example | |
| 246 | |
| 247 @noindent | |
| 248 produces the error message | |
| 249 | |
| 250 @example | |
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251 @group |
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252 parse error: |
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253 |
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254 syntax error |
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255 |
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256 >>> [ 1 a ' ] |
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257 ^ |
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258 @end group |
| 3294 | 259 @end example |
| 260 | |
| 261 @noindent | |
| 6620 | 262 because not doing so would cause trouble when parsing the valid expression |
| 3294 | 263 |
| 264 @example | |
| 265 [ a 'foo' ] | |
| 266 @end example | |
| 267 | |
| 268 For clarity, it is probably best to always use commas and semicolons to | |
| 4476 | 269 separate matrix elements and rows. |
| 3294 | 270 |
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271 The maximum number of elements in a matrix is fixed when Octave is compiled. |
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272 The allowable number can be queried with the function @code{sizemax}. Note |
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273 that other factors, such as the amount of memory available on your machine, |
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274 may limit the maximum size of matrices to something smaller. |
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275 |
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276 @DOCSTRING(sizemax) |
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277 |
| 3294 | 278 When you type a matrix or the name of a variable whose value is a |
| 279 matrix, Octave responds by printing the matrix in with neatly aligned | |
| 280 rows and columns. If the rows of the matrix are too large to fit on the | |
| 281 screen, Octave splits the matrix and displays a header before each | |
| 282 section to indicate which columns are being displayed. You can use the | |
| 283 following variables to control the format of the output. | |
| 284 | |
| 3321 | 285 @DOCSTRING(output_max_field_width) |
| 3294 | 286 |
| 3321 | 287 @DOCSTRING(output_precision) |
| 3294 | 288 |
| 289 It is possible to achieve a wide range of output styles by using | |
| 290 different values of @code{output_precision} and | |
| 291 @code{output_max_field_width}. Reasonable combinations can be set using | |
| 292 the @code{format} function. @xref{Basic Input and Output}. | |
| 293 | |
| 3321 | 294 @DOCSTRING(split_long_rows) |
| 3294 | 295 |
| 296 Octave automatically switches to scientific notation when values become | |
| 297 very large or very small. This guarantees that you will see several | |
| 298 significant figures for every value in a matrix. If you would prefer to | |
| 299 see all values in a matrix printed in a fixed point format, you can set | |
| 300 the built-in variable @code{fixed_point_format} to a nonzero value. But | |
| 301 doing so is not recommended, because it can produce output that can | |
| 302 easily be misinterpreted. | |
| 303 | |
| 3321 | 304 @DOCSTRING(fixed_point_format) |
| 3294 | 305 |
| 306 @menu | |
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307 * Empty Matrices:: |
| 3294 | 308 @end menu |
| 309 | |
| 4167 | 310 @node Empty Matrices |
| 3294 | 311 @subsection Empty Matrices |
| 312 | |
| 313 A matrix may have one or both dimensions zero, and operations on empty | |
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314 matrices are handled as described by Carl @nospell{de} Boor in @cite{An Empty |
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315 Exercise}, SIGNUM, Volume 25, pages 2-6, 1990 and C. N. Nett and W. M. |
| 3294 | 316 Haddad, in @cite{A System-Theoretic Appropriate Realization of the Empty |
| 317 Matrix Concept}, IEEE Transactions on Automatic Control, Volume 38, | |
| 318 Number 5, May 1993. | |
| 319 @tex | |
| 320 Briefly, given a scalar $s$, an $m\times n$ matrix $M_{m\times n}$, | |
| 321 and an $m\times n$ empty matrix $[\,]_{m\times n}$ (with either one or | |
| 322 both dimensions equal to zero), the following are true: | |
| 323 $$ | |
| 324 \eqalign{% | |
| 325 s \cdot [\,]_{m\times n} = [\,]_{m\times n} \cdot s &= [\,]_{m\times n}\cr | |
| 326 [\,]_{m\times n} + [\,]_{m\times n} &= [\,]_{m\times n}\cr | |
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327 [\,]_{0\times m} \cdot M_{m\times n} &= [\,]_{0\times n}\cr |
| 3294 | 328 M_{m\times n} \cdot [\,]_{n\times 0} &= [\,]_{m\times 0}\cr |
| 329 [\,]_{m\times 0} \cdot [\,]_{0\times n} &= 0_{m\times n}} | |
| 330 $$ | |
| 331 @end tex | |
| 6620 | 332 @ifnottex |
| 3294 | 333 Briefly, given a scalar @var{s}, an @var{m} by |
| 334 @var{n} matrix @code{M(mxn)}, and an @var{m} by @var{n} empty matrix | |
| 335 @code{[](mxn)} (with either one or both dimensions equal to zero), the | |
| 336 following are true: | |
| 337 | |
| 338 @example | |
| 339 @group | |
| 340 s * [](mxn) = [](mxn) * s = [](mxn) | |
| 341 | |
| 342 [](mxn) + [](mxn) = [](mxn) | |
| 343 | |
| 344 [](0xm) * M(mxn) = [](0xn) | |
| 345 | |
| 346 M(mxn) * [](nx0) = [](mx0) | |
| 347 | |
| 348 [](mx0) * [](0xn) = 0(mxn) | |
| 349 @end group | |
| 350 @end example | |
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351 |
| 6620 | 352 @end ifnottex |
| 3294 | 353 |
| 354 By default, dimensions of the empty matrix are printed along with the | |
| 355 empty matrix symbol, @samp{[]}. The built-in variable | |
| 356 @code{print_empty_dimensions} controls this behavior. | |
| 357 | |
| 3321 | 358 @DOCSTRING(print_empty_dimensions) |
| 3294 | 359 |
| 360 Empty matrices may also be used in assignment statements as a convenient | |
| 361 way to delete rows or columns of matrices. | |
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362 @xref{Assignment Ops,,Assignment Expressions}. |
| 3294 | 363 |
| 364 When Octave parses a matrix expression, it examines the elements of the | |
| 365 list to determine whether they are all constants. If they are, it | |
| 366 replaces the list with a single matrix constant. | |
| 367 | |
| 4167 | 368 @node Ranges |
| 3294 | 369 @section Ranges |
| 370 @cindex range expressions | |
| 371 @cindex expression, range | |
| 372 | |
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373 @opindex : |
| 3294 | 374 |
| 375 A @dfn{range} is a convenient way to write a row vector with evenly | |
| 376 spaced elements. A range expression is defined by the value of the first | |
| 377 element in the range, an optional value for the increment between | |
| 378 elements, and a maximum value which the elements of the range will not | |
| 379 exceed. The base, increment, and limit are separated by colons (the | |
| 380 @samp{:} character) and may contain any arithmetic expressions and | |
| 381 function calls. If the increment is omitted, it is assumed to be 1. | |
| 382 For example, the range | |
| 383 | |
| 384 @example | |
| 385 1 : 5 | |
| 386 @end example | |
| 387 | |
| 388 @noindent | |
| 389 defines the set of values @samp{[ 1, 2, 3, 4, 5 ]}, and the range | |
| 390 | |
| 391 @example | |
| 392 1 : 3 : 5 | |
| 393 @end example | |
| 394 | |
| 395 @noindent | |
| 396 defines the set of values @samp{[ 1, 4 ]}. | |
| 397 | |
| 398 Although a range constant specifies a row vector, Octave does @emph{not} | |
| 399 convert range constants to vectors unless it is necessary to do so. | |
| 400 This allows you to write a constant like @samp{1 : 10000} without using | |
| 401 80,000 bytes of storage on a typical 32-bit workstation. | |
| 402 | |
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403 A common example of when it does become necessary to convert ranges into |
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404 vectors occurs when they appear within a vector (i.e., inside square |
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405 brackets). For instance, whereas |
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406 |
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407 @example |
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408 x = 0 : 0.1 : 1; |
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409 @end example |
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410 |
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411 @noindent |
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412 defines @var{x} to be a variable of type @code{range} and occupies 24 |
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413 bytes of memory, the expression |
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414 |
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415 @example |
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416 y = [ 0 : 0.1 : 1]; |
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417 @end example |
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418 |
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419 @noindent |
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420 defines @var{y} to be of type @code{matrix} and occupies 88 bytes of |
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421 memory. |
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422 |
| 3294 | 423 Note that the upper (or lower, if the increment is negative) bound on |
| 424 the range is not always included in the set of values, and that ranges | |
| 425 defined by floating point values can produce surprising results because | |
| 426 Octave uses floating point arithmetic to compute the values in the | |
| 427 range. If it is important to include the endpoints of a range and the | |
| 428 number of elements is known, you should use the @code{linspace} function | |
| 429 instead (@pxref{Special Utility Matrices}). | |
| 430 | |
| 9158 | 431 When adding a scalar to a range, subtracting a scalar from it (or subtracting a |
| 432 range from a scalar) and multiplying by scalar, Octave will attempt to avoid | |
| 433 unpacking the range and keep the result as a range, too, if it can determine | |
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434 that it is safe to do so. For instance, doing |
| 9158 | 435 |
| 436 @example | |
| 437 a = 2*(1:1e7) - 1; | |
| 438 @end example | |
| 439 | |
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440 @noindent |
| 9158 | 441 will produce the same result as @samp{1:2:2e7-1}, but without ever forming a |
| 442 vector with ten million elements. | |
| 443 | |
| 444 Using zero as an increment in the colon notation, as @samp{1:0:1} is not | |
| 445 allowed, because a division by zero would occur in determining the number of | |
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446 range elements. However, ranges with zero increment (i.e., all elements equal) |
| 9158 | 447 are useful, especially in indexing, and Octave allows them to be constructed |
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448 using the built-in function @dfn{ones}. Note that because a range must be a row |
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449 vector, @samp{ones (1, 10)} produces a range, while @samp{ones (10, 1)} does |
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450 not. |
| 9158 | 451 |
| 3294 | 452 When Octave parses a range expression, it examines the elements of the |
| 453 expression to determine whether they are all constants. If they are, it | |
| 454 replaces the range expression with a single range constant. | |
| 455 | |
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456 @node Single Precision Data Types |
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457 @section Single Precision Data Types |
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458 |
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459 Octave includes support for single precision data types, and most of the |
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460 functions in Octave accept single precision values and return single |
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461 precision answers. A single precision variable is created with the |
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462 @code{single} function. |
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463 |
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464 @DOCSTRING(single) |
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465 |
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466 for example: |
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467 |
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468 @example |
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469 @group |
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470 sngl = single (rand (2, 2)) |
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471 @result{} sngl = |
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472 0.37569 0.92982 |
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473 0.11962 0.50876 |
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474 class (sngl) |
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475 @result{} single |
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476 @end group |
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477 @end example |
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478 |
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479 Many functions can also return single precision values directly. For |
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480 example |
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481 |
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482 @example |
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483 @group |
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484 ones (2, 2, "single") |
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485 zeros (2, 2, "single") |
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486 eye (2, 2, "single") |
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487 rand (2, 2, "single") |
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488 NaN (2, 2, "single") |
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489 NA (2, 2, "single") |
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490 Inf (2, 2, "single") |
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491 @end group |
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492 @end example |
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493 |
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494 @noindent |
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495 will all return single precision matrices. |
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496 |
| 6549 | 497 @node Integer Data Types |
| 498 @section Integer Data Types | |
| 499 | |
| 6620 | 500 Octave supports integer matrices as an alternative to using double |
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501 precision. It is possible to use both signed and unsigned integers |
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502 represented by 8, 16, 32, or 64 bits. It should be noted that most |
| 6620 | 503 computations require floating point data, meaning that integers will |
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504 often change type when involved in numeric computations. For this |
| 6620 | 505 reason integers are most often used to store data, and not for |
| 506 calculations. | |
| 507 | |
| 508 In general most integer matrices are created by casting | |
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509 existing matrices to integers. The following example shows how to cast |
| 6620 | 510 a matrix into 32 bit integers. |
| 511 | |
| 512 @example | |
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513 @group |
| 6620 | 514 float = rand (2, 2) |
| 515 @result{} float = 0.37569 0.92982 | |
| 516 0.11962 0.50876 | |
| 517 integer = int32 (float) | |
| 518 @result{} integer = 0 1 | |
| 519 0 1 | |
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520 @end group |
| 6620 | 521 @end example |
| 522 | |
| 523 @noindent | |
| 524 As can be seen, floating point values are rounded to the nearest integer | |
| 525 when converted. | |
| 526 | |
| 6549 | 527 @DOCSTRING(isinteger) |
| 528 | |
| 529 @DOCSTRING(int8) | |
| 530 | |
| 531 @DOCSTRING(uint8) | |
| 532 | |
| 533 @DOCSTRING(int16) | |
| 534 | |
| 535 @DOCSTRING(uint16) | |
| 536 | |
| 537 @DOCSTRING(int32) | |
| 538 | |
| 539 @DOCSTRING(uint32) | |
| 540 | |
| 541 @DOCSTRING(int64) | |
| 542 | |
| 543 @DOCSTRING(uint64) | |
| 544 | |
| 545 @DOCSTRING(intmax) | |
| 546 | |
| 547 @DOCSTRING(intmin) | |
| 548 | |
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549 @DOCSTRING(flintmax) |
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550 |
| 6624 | 551 @menu |
| 552 * Integer Arithmetic:: | |
| 553 @end menu | |
| 554 | |
| 6620 | 555 @node Integer Arithmetic |
| 556 @subsection Integer Arithmetic | |
| 557 | |
| 558 While many numerical computations can't be carried out in integers, | |
| 559 Octave does support basic operations like addition and multiplication | |
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560 on integers. The operators @code{+}, @code{-}, @code{.*}, and @code{./} |
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561 work on integers of the same type. So, it is possible to add two 32 bit |
| 6620 | 562 integers, but not to add a 32 bit integer and a 16 bit integer. |
| 563 | |
| 564 When doing integer arithmetic one should consider the possibility of | |
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565 underflow and overflow. This happens when the result of the computation |
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566 can't be represented using the chosen integer type. As an example it is |
| 6620 | 567 not possible to represent the result of @math{10 - 20} when using |
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568 unsigned integers. Octave makes sure that the result of integer |
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569 computations is the integer that is closest to the true result. So, the |
| 6620 | 570 result of @math{10 - 20} when using unsigned integers is zero. |
| 571 | |
| 572 When doing integer division Octave will round the result to the nearest | |
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573 integer. This is different from most programming languages, where the |
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574 result is often floored to the nearest integer. So, the result of |
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575 @code{int32 (5) ./ int32 (8)} is @code{1}. |
| 6620 | 576 |
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577 @DOCSTRING(idivide) |
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578 |
| 6781 | 579 @node Bit Manipulations |
| 580 @section Bit Manipulations | |
| 581 | |
| 582 Octave provides a number of functions for the manipulation of numeric | |
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583 values on a bit by bit basis. The basic functions to set and obtain the |
| 6781 | 584 values of individual bits are @code{bitset} and @code{bitget}. |
| 585 | |
| 586 @DOCSTRING(bitset) | |
| 587 | |
| 588 @DOCSTRING(bitget) | |
| 589 | |
| 590 The arguments to all of Octave's bitwise operations can be scalar or | |
| 591 arrays, except for @code{bitcmp}, whose @var{k} argument must a | |
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592 scalar. In the case where more than one argument is an array, then all |
| 6781 | 593 arguments must have the same shape, and the bitwise operator is applied |
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594 to each of the elements of the argument individually. If at least one |
| 6781 | 595 argument is a scalar and one an array, then the scalar argument is |
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596 duplicated. Therefore |
| 6781 | 597 |
| 598 @example | |
| 599 bitget (100, 8:-1:1) | |
| 600 @end example | |
| 601 | |
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602 @noindent |
| 6781 | 603 is the same as |
| 604 | |
| 605 @example | |
| 606 bitget (100 * ones (1, 8), 8:-1:1) | |
| 607 @end example | |
| 608 | |
| 609 It should be noted that all values passed to the bit manipulation | |
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610 functions of Octave are treated as integers. Therefore, even though the |
| 6781 | 611 example for @code{bitset} above passes the floating point value |
| 612 @code{10}, it is treated as the bits @code{[1, 0, 1, 0]} rather than the | |
| 613 bits of the native floating point format representation of @code{10}. | |
| 614 | |
| 8828 | 615 As the maximum value that can be represented by a number is important |
| 6781 | 616 for bit manipulation, particularly when forming masks, Octave supplies |
| 617 the function @code{bitmax}. | |
| 618 | |
| 619 @DOCSTRING(bitmax) | |
| 620 | |
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621 This is the double precision version of the function @code{intmax}, |
| 6781 | 622 previously discussed. |
| 623 | |
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624 Octave also includes the basic bitwise 'and', 'or', and 'exclusive or' |
| 6781 | 625 operators. |
| 626 | |
| 627 @DOCSTRING(bitand) | |
| 628 | |
| 629 @DOCSTRING(bitor) | |
| 630 | |
| 631 @DOCSTRING(bitxor) | |
| 632 | |
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633 The bitwise 'not' operator is a unary operator that performs a logical |
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634 negation of each of the bits of the value. For this to make sense, the |
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635 mask against which the value is negated must be defined. Octave's |
| 6781 | 636 bitwise 'not' operator is @code{bitcmp}. |
| 637 | |
| 638 @DOCSTRING(bitcmp) | |
| 639 | |
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640 Octave also includes the ability to left-shift and right-shift values bitwise. |
| 6781 | 641 |
| 642 @DOCSTRING(bitshift) | |
| 643 | |
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644 Bits that are shifted out of either end of the value are lost. Octave |
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645 also uses arithmetic shifts, where the sign bit of the value is kept |
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646 during a right shift. For example: |
| 6781 | 647 |
| 648 @example | |
| 649 @group | |
| 650 bitshift (-10, -1) | |
| 651 @result{} -5 | |
| 652 bitshift (int8 (-1), -1) | |
| 653 @result{} -1 | |
| 654 @end group | |
| 655 @end example | |
| 656 | |
| 657 Note that @code{bitshift (int8 (-1), -1)} is @code{-1} since the bit | |
| 658 representation of @code{-1} in the @code{int8} data type is @code{[1, 1, | |
| 659 1, 1, 1, 1, 1, 1]}. | |
| 660 | |
| 4167 | 661 @node Logical Values |
| 3428 | 662 @section Logical Values |
| 663 | |
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664 Octave has built-in support for logical values, i.e., variables that |
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665 are either @code{true} or @code{false}. When comparing two variables, |
| 6620 | 666 the result will be a logical value whose value depends on whether or |
| 667 not the comparison is true. | |
| 668 | |
| 669 The basic logical operations are @code{&}, @code{|}, and @code{!}, | |
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670 which correspond to ``Logical And'', ``Logical Or'', and ``Logical |
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671 Negation''. These operations all follow the usual rules of logic. |
| 6620 | 672 |
| 673 It is also possible to use logical values as part of standard numerical | |
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674 calculations. In this case @code{true} is converted to @code{1}, and |
| 6620 | 675 @code{false} to 0, both represented using double precision floating |
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676 point numbers. So, the result of @code{true*22 - false/6} is @code{22}. |
| 6620 | 677 |
| 678 Logical values can also be used to index matrices and cell arrays. | |
| 679 When indexing with a logical array the result will be a vector containing | |
| 680 the values corresponding to @code{true} parts of the logical array. | |
| 681 The following example illustrates this. | |
| 682 | |
| 683 @example | |
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684 @group |
| 6620 | 685 data = [ 1, 2; 3, 4 ]; |
| 686 idx = (data <= 2); | |
| 687 data(idx) | |
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688 @result{} ans = [ 1; 2 ] |
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689 @end group |
| 6620 | 690 @end example |
| 691 | |
| 692 @noindent | |
| 693 Instead of creating the @code{idx} array it is possible to replace | |
|
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694 @code{data(idx)} with @w{@code{data( data <= 2 )}} in the above code. |
| 6620 | 695 |
| 8828 | 696 Logical values can also be constructed by |
| 6620 | 697 casting numeric objects to logical values, or by using the @code{true} |
| 698 or @code{false} functions. | |
| 699 | |
| 6549 | 700 @DOCSTRING(logical) |
| 701 | |
| 3428 | 702 @DOCSTRING(true) |
| 703 | |
| 704 @DOCSTRING(false) | |
| 705 | |
|
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706 @node Promotion and Demotion of Data Types |
|
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|
707 @section Promotion and Demotion of Data Types |
|
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708 |
|
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|
709 Many operators and functions can work with mixed data types. For example, |
|
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710 |
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711 @example |
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712 @group |
|
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713 uint8 (1) + 1 |
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714 @result{} 2 |
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715 @end group |
|
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|
716 @end example |
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|
717 |
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|
718 @noindent |
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|
719 where the above operator works with an 8-bit integer and a double precision |
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720 value and returns an 8-bit integer value. Note that the type is demoted |
|
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721 to an 8-bit integer, rather than promoted to a double precision value as |
|
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722 might be expected. The reason is that if Octave promoted values in |
|
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|
723 expressions like the above with all numerical constants would need to be |
|
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|
724 explicitly cast to the appropriate data type like |
|
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|
725 |
|
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|
726 @example |
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727 @group |
|
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|
728 uint8 (1) + uint8 (1) |
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729 @result{} 2 |
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730 @end group |
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|
731 @end example |
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732 |
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|
733 @noindent |
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|
734 which becomes difficult for the user to apply uniformly and might allow |
|
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735 hard to find bugs to be introduced. The same applies to single precision |
|
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736 values where a mixed operation such as |
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737 |
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738 @example |
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739 @group |
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740 single (1) + 1 |
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741 @result{} 2 |
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742 @end group |
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|
743 @end example |
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744 |
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|
745 @noindent |
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746 returns a single precision value. The mixed operations that are valid |
|
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|
747 and their returned data types are |
|
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|
748 |
|
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|
749 @multitable @columnfractions .2 .3 .3 .2 |
|
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750 @headitem @tab Mixed Operation @tab Result @tab |
|
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751 @item @tab double OP single @tab single @tab |
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752 @item @tab double OP integer @tab integer @tab |
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753 @item @tab double OP char @tab double @tab |
|
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754 @item @tab double OP logical @tab double @tab |
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|
755 @item @tab single OP integer @tab integer @tab |
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|
756 @item @tab single OP char @tab single @tab |
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757 @item @tab single OP logical @tab single @tab |
|
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758 @end multitable |
|
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|
759 |
|
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|
760 The same logic applies to functions with mixed arguments such as |
|
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|
761 |
|
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762 @example |
|
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763 @group |
|
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|
764 min (single (1), 0) |
|
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765 @result{} 0 |
|
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766 @end group |
|
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767 @end example |
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768 |
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|
769 @noindent |
|
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|
770 where the returned value is single precision. |
|
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|
771 |
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|
772 In the case of mixed type indexed assignments, the type is not |
|
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773 changed. For example, |
|
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|
774 |
|
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775 @example |
|
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776 @group |
|
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|
777 x = ones (2, 2); |
|
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778 x(1, 1) = single (2) |
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|
779 @result{} x = 2 1 |
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780 1 1 |
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781 @end group |
|
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782 @end example |
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783 |
|
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784 @noindent |
|
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785 where @code{x} remains of the double precision type. |
|
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786 |
| 4167 | 787 @node Predicates for Numeric Objects |
| 3294 | 788 @section Predicates for Numeric Objects |
| 789 | |
| 6620 | 790 Since the type of a variable may change during the execution of a |
|
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|
791 program, it can be necessary to do type checking at run-time. Doing this |
|
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792 also allows you to change the behavior of a function depending on the |
|
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793 type of the input. As an example, this naive implementation of @code{abs} |
| 7001 | 794 returns the absolute value of the input if it is a real number, and the |
| 6620 | 795 length of the input if it is a complex number. |
| 796 | |
| 797 @example | |
|
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|
798 @group |
| 6620 | 799 function a = abs (x) |
| 800 if (isreal (x)) | |
| 801 a = sign (x) .* x; | |
| 802 elseif (iscomplex (x)) | |
| 803 a = sqrt (real(x).^2 + imag(x).^2); | |
| 804 endif | |
| 805 endfunction | |
|
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806 @end group |
| 6620 | 807 @end example |
| 808 | |
| 809 The following functions are available for determining the type of a | |
| 810 variable. | |
| 811 | |
| 3428 | 812 @DOCSTRING(isnumeric) |
| 813 | |
|
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814 @DOCSTRING(isfloat) |
| 3428 | 815 |
|
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|
816 @DOCSTRING(isreal) |
|
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817 |
| 4029 | 818 @DOCSTRING(iscomplex) |
| 3428 | 819 |
| 4029 | 820 @DOCSTRING(ismatrix) |
| 3294 | 821 |
| 4029 | 822 @DOCSTRING(isvector) |
| 3294 | 823 |
|
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824 @DOCSTRING(isrow) |
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825 |
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826 @DOCSTRING(iscolumn) |
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|
827 |
| 4029 | 828 @DOCSTRING(isscalar) |
| 3294 | 829 |
| 4029 | 830 @DOCSTRING(issquare) |
| 3294 | 831 |
| 4029 | 832 @DOCSTRING(issymmetric) |
| 3428 | 833 |
|
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834 @DOCSTRING(ishermitian) |
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|
835 |
| 6550 | 836 @DOCSTRING(isdefinite) |
| 837 | |
| 6688 | 838 @DOCSTRING(islogical) |
| 6550 | 839 |
| 840 @DOCSTRING(isprime) | |
|
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841 |
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|
842 If instead of knowing properties of variables, you wish to know which |
|
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|
843 variables are defined and to gather other information about the |
|
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|
844 workspace itself, @pxref{Status of Variables}. |